On Cryptographic Parameters of Permutation Polynomials of the form <i>x<sup>r</sup>h</i>(<i>x</i><sup>(2<i><sup>n</sup></i>-1)/<i>d</i></sup>)

DOI Web Site 参考文献26件
  • JEONG Jaeseong
    Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University
  • KIM Chang Heon
    Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University
  • KOO Namhun
    Institute of Mathematical Sciences, Ewha Womans University
  • KWON Soonhak
    Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University
  • LEE Sumin
    Applied Algebra and Optimization Research Center (AORC), Sungkyunkwan University

抄録

<p>The differential uniformity, the boomerang uniformity, and the extended Walsh spectrum etc are important parameters to evaluate the security of S (substitution)-box. In this paper, we introduce efficient formulas to compute these cryptographic parameters of permutation polynomials of the form xrh(x(2<sup>n-1)/d</sup>) over a finite field of q=2n elements, where r is a positive integer and d is a positive divisor of 2n-1. The computational cost of those formulas is proportional to d. We investigate differentially 4-uniform permutation polynomials of the form xrh(x(2<sup>n-1)/3</sup>) and compute the boomerang spectrum and the extended Walsh spectrum of them using the suggested formulas when 6≤n≤12 is even, where d=3 is the smallest nontrivial d for even n. We also investigate the differential uniformity of some permutation polynomials introduced in some recent papers for the case d=2n/2+1.</p>

収録刊行物

参考文献 (26)*注記

もっと見る

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ